Writing Polynomial Functions from Complex Roots — Quiz
Question 2 • Algebra 2 with Probability
Which polynomial function f of x has a leading coefficient of 1 , roots negative 4 , 2 , and 9 with multiplicity 1 , and root negative 5 with multiplicity 3 ?
Answer
A
f of x is equal to 3 open paren x plus 5 close paren open paren x plus 4 close paren open paren x minus 2 close paren open paren x minus 9 close paren
B
f of x is equal to 3 open paren x minus 5 close paren open paren x minus 4 close paren open paren x plus 2 close paren open paren x plus 9 close paren
C
f of x is equal to open paren x plus 5 close paren times open paren x plus 5 close paren times open paren x plus 5 close paren times open paren x plus 4 close paren times open paren x minus 2 close paren times open paren x minus 9 close paren
D
f of x is equal to open paren x minus 5 close paren times open paren x minus 5 close paren times open paren x minus 5 close paren times open paren x minus 4 close paren times open paren x plus 2 close paren times open paren x plus 9 close paren
Explanation
A root r gives a factor (x − r), so the roots −4, 2, and 9 give factors (x + 4), (x − 2), and (x − 9). The root −5 with multiplicity 3 gives the factor (x + 5)³. Multiplying these factors with leading coefficient 1 gives choice C.
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